# How do you find the product of (2+v)^2?

Apr 7, 2018

${v}^{2} + 4 v + 4$

#### Explanation:

First:

${\left(v + 2\right)}^{2} = \left(v + 2\right) \left(v + 2\right)$

Now expand out using FOIL or another method you have been taught...

$\left(\textcolor{red}{v} + \textcolor{b l u e}{2}\right) \left(\textcolor{g r e e n}{v} + \textcolor{\mathmr{and} a n \ge}{2}\right)$

$\implies \textcolor{red}{v} \textcolor{g r e e n}{v} + \textcolor{\mathmr{and} a n \ge}{2} \textcolor{red}{v} + \textcolor{b l u e}{2} \textcolor{g r e e n}{v} + 2 \times 2$

$\implies {v}^{2} + 4 v + 4$

Apr 7, 2018

The product of ${\left(2 + v\right)}^{2}$ is ${v}^{2} + 4 v + 4$.

#### Explanation:

The formula for squaring a binomial is as follows:
${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$

Thus,
${\left(2 + v\right)}^{2}$
$= {2}^{2} + 2 \cdot 2 \cdot v + {v}^{2}$
$= 4 + 4 v + {v}^{2}$
$= {v}^{2} + 4 v + 4$